Wannier representation of Z2 topological insulators

Alexey A. Soluyanov, David Vanderbilt

Research output: Contribution to journalArticle

146 Scopus citations


We consider the problem of constructing Wannier functions for Z2 topological insulators in two dimensions. It is well known that there is a topological obstruction to the construction of Wannier functions for Chern insulators, but it has been unclear whether this is also true for the Z 2case. We consider the Kane-Mele tight-binding model, which exhibits both normal (Z2-even) and topological (Z2-odd) phases as a function of the model parameters. In the Z2-even phase, the usual projection-based scheme can be used to build the Wannier representation. In the Z2-odd phase, we do find a topological obstruction, but only if one insists on choosing a gauge that respects the time-reversal symmetry, corresponding to Wannier functions that come in time-reversal pairs. If, instead, we are willing to violate this gauge condition, a Wannier representation becomes possible. We present an explicit construction of Wannier functions for the Z2-odd phase of the Kane-Mele model via a modified projection scheme, followed by maximal localization, and confirm that these Wannier functions correctly represent the electric polarization and other electronic properties of the insulator.

Original languageEnglish (US)
Article number035108
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number3
StatePublished - Jan 13 2011

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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